AMSCO'S Geometry. New York - Rye High School

Equidistant Lines in Coordinate Geometry 6232. Ryan said that if the locus of points equidistant from y x 2 and y x 10 is y x 6,then the distance from y x 6 to y x 2 and to y x 10 is 4. Do you agree withRyan? Justify your answer.Developing SkillsIn 3–8, find the equation of the locus of points equidistant from each given pair of points.3. (1, 1) and (9, 1) 4. (3, 1) and (3, 3) 5. (0, 2) and (2, 0)6. (0, 6) and (4, 2) 7. (2, 2) and (0, 2) 8. (4, 5) and (2, 1)In 9–14, find the equation of the locus of points equidistant from each given pair of parallel lines9. x 1 and x 7 10. y 0 and y 611. y x 3 and y x 9 12. y x 2 and y x 613. y 2x 1 and y 2x 5 14. 2x y 7 and y 2x 915. Find the coordinates of the locus of points equidistant from (2, 3) and (4, 3), and 3 unitsfrom (1, 3).16. Find the coordinates of the locus of points equidistant from (2, 5) and (2, 3), and 4 unitsfrom (0, 1).Applying Skills17. a. Find the equation of the locus of points equidistant from (3, 1) and (5, 5).b. Prove that the point (2, 6) is equidistant from the points (3, 1) and (5, 5) by showingthat it lies on the line whose equation you wrote in a.c. Prove that the point (2, 6) is equidistant from (3, 1) and (5, 5) by using the distance formula.18. a. Find the equation of the locus of points equidistant from the parallel lines y x 3 andy x 5.b. Show that point P(3, 2) is equidistant from the given parallel lines by showing that it lieson the line whose equation you wrote in a.c. Find the equation of the line that is perpendicular to the given parallel lines throughpoint P(3, 2).d. Find the coordinates of point A at which the line whose equation you wrote in c intersectsy x 3.e. Find the coordinates of point B at which the line whose equation you wrote in c intersectsy x 5.f. Use the distance formula to show that PA PB, that is, that P is equidistant fromy x 3 and y x 5.19. Show that the locus of points equidistant from the line y x 1 and the line y x 1 isthe y-axis and the line y 1.